Magnetocaloric effect and refrigerant capacity in charge-ordered manganites

Abstract

The influence of first- and second-order magnetic phase transitions on the magnetocaloric effect (MCE) and refrigerant capacity (RC) of charge-ordered Pr0.5Sr0.5MnO3 has been investigated. The system undergoes a paramagnetic to ferromagnetic transition at TC∼255 K followed by a ferromagnetic charge-disordered to antiferromagnetic charge-ordered transition at TCO∼165 K. While the first-order magnetic transition (FOMT) at TCO induces a larger MCE (6.8 J/kg K) limited to a narrower temperature range resulting in a smaller RC (168 J/kg), the second-order magnetic transition at TC induces a smaller MCE (3.2 J/kg K) but spreads over a broader temperature range resulting in a larger RC (215 J/kg). In addition, large magnetic and thermal hysteretic losses associated with the FOMT below TCO are detrimental to an efficient magnetic RC, whereas these effects are negligible below TC because of the second-order nature of this transition. These results are of practical importance in assessing the usefulness of charge-ordered manganite materials for active magnetic refrigeration, and Pr0.5Sr0.5MnO3 provides an interesting case study in which the influence of first- and second-order transitions on MCE could be compared in the same system in a single experiment.

Full text

Magnetocaloric effect and refrigerant capacity in charge-ordered manganites
N. S. Bingham, M. H. Phan, H. Srikanth, , M. A. Torija, and C. Leighton
Citation: Journal of Applied Physics 106, 023909 (2009); doi: 10.1063/1.3174396
View online: http://dx.doi.org/10.1063/1.3174396
View Table of Contents: http://aip.scitation.org/toc/jap/106/2
Published by the American Institute of Physics
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Magnetocaloric effect and refrigerant capacity in charge-ordered
manganites
N. S. Bingham,1M. H. Phan,1H. Srikanth,1,a兲M. A. Torija,2and C. Leighton2
1Department of Physics, University of South Florida, Tampa, Florida 33620, USA
2Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis,
Minnesota 55455, USA
共Received 11 April 2009; accepted 11 June 2009; published online 17 July 2009兲
The influence of first- and second-order magnetic phase transitions on the magnetocaloric effect
共MCE兲and refrigerant capacity 共RC兲of charge-ordered Pr0.5Sr0.5MnO3has been investigated. The
system undergoes a paramagnetic to ferromagnetic transition at TC⬃255 K followed by a
ferromagnetic charge-disordered to antiferromagnetic charge-ordered transition at TCO⬃165 K.
While the first-order magnetic transition 共FOMT兲at TCO induces a larger MCE 共6.8 J/kg K兲limited
to a narrower temperature range resulting in a smaller RC 共168 J/kg兲, the second-order magnetic
transition at TCinduces a smaller MCE 共3.2 J/kg K兲but spreads over a broader temperature range
resulting in a larger RC 共215 J/kg兲. In addition, large magnetic and thermal hysteretic losses
associated with the FOMT below TCO are detrimental to an efficient magnetic RC, whereas these
effects are negligible below TCbecause of the second-order nature of this transition. These results
are of practical importance in assessing the usefulness of charge-ordered manganite materials for
active magnetic refrigeration, and Pr0.5Sr0.5MnO3provides an interesting case study in which the
influence of first- and second-order transitions on MCE could be compared in the same system in a
single experiment. © 2009 American Institute of Physics.关DOI: 10.1063/1.3174396兴
I. INTRODUCTION
Doped manganites with a general formula of
R1−xMxMnO3共R=La, Pr, Nd, etc., and M=Sr, Ca, Ba, etc.兲
exhibit a rich variety of phenomena such as colossal
magnetoresistance1and large magnetocaloric effect 共MCE兲.2
The latter effect, which is represented by an isothermal
change in magnetic entropy or an adiabatic change in tem-
perature in magnetic fields, forms the basis for magnetic
refrigeration.3Manganites are relatively easy to synthesize,
are tunable by adjustment of the doping concentration, and
are considered promising candidates for magnetic refrigera-
tion at various temperatures, as reviewed by Phan and Yu.2
Recently, half-doped R0.5M0.5MnO3manganites that ex-
hibit a giant magnetic entropy change 共⌬SM兲in the vicinity
of the charge-ordered 共CO兲transition have attracted
attention.4–9Sande et al.4reported values of ⌬SM
⬃2.8 J/kg K in Nd0.5Sr0.5MnO3around the antiferromag-
netic 共AFM兲CO to ferromagnetic 共FM兲charge-disordered
transition temperature, TCO 关the first-order magnetic transi-
tion 共FOMT兲兴, which was about three times larger than that
共0.9 J/kg K兲obtained around the paramagnetic to FM transi-
tion temperature, TC关the second-order magnetic transition
共SOMT兲兴, for a field change of 1 T. A similar trend has also
been observed in other CO manganites.5–9This leads to a
general expectation that the consistently larger values of ⌬SM
around TCO would be more useful for magnetic refrigeration
than those around TC.
However, in assessing the usefulness of a magnetic re-
frigerant material, the refrigerant capacity 共RC兲, which is a
measure of the amount of heat transfer between the cold and
hot sinks in an ideal refrigeration cycle, is considered to be
the most important factor.10–12 The RC depends not only on
the magnitude of ⌬SM, but also on the temperature depen-
dence of ⌬SM共e.g., the full width at half maximum of the
⌬SM共T兲peak兲.10,12 In this context, a good magnetic refriger-
ant material with large RC requires both a large magnitude of
⌬SMas well as a broad width of the ⌬SM共T兲curve. Most
previous studies on CO manganites4–9were focused mainly
on exploring large MCE 共large magnitudes of ⌬SM兲around
TCO and did not consider in detail the issues of RC and
hysteretic losses. Thus, from fundamental and practical per-
spectives, it is essential to understand the influence of the
magnetic phase transitions on both the MCE and RC in these
materials.
In this paper, we present systematic studies of the influ-
ence of the FOMT and SOMT on the MCE and RC of CO
Pr0.5Sr0.5MnO3. Our results reveal that while the FOMT at
TCO induces a larger MCE, it is restricted to a narrow tem-
perature range resulting in a smaller RC. The SOMT at TC
induces a smaller MCE but with a distribution over a broader
temperature range, thus resulting in a larger RC. In addition,
hysteretic losses associated with the FOMT are very large
below TCO and therefore detrimental to the RC, whereas
these effects are very small or negligible below TCdue to the
nature of the SOMT.
II. THEORETICAL BACKGROUND
The change in the entropy 共S兲of a magnetic material in
a magnetic field 共H兲is related to that of magnetization 共M兲
with respect to temperature 共T兲through the thermodynamic
Maxwell relation,
a兲Electronic mail: sharihar@cas.usf.edu.
JOURNAL OF APPLIED PHYSICS 106, 023909 共2009兲
0021-8979/2009/106共2兲/023909/5/$25.00 © 2009 American Institute of Physics106, 023909-1

冉
⳵
S共T,H兲
⳵
H
冊
T
=
冉
⳵
M共T,H兲
⳵
T
冊
H
.共1兲
The change in magnetic entropy, ⌬SM, caused by the varia-
tion in applied magnetic field from 0 to H0, is calculated as
⌬SM共T,H0兲=SM共T,H0兲−SM共T,0兲
=
␮
0
冕
0
H0
冉
⳵
M共T,H兲
⳵
T
冊
H
dH,共2兲
with
␮
0being the permeability in vacuum. For magnetization
measurements made at discrete field and temperature inter-
vals, ⌬SMcan be approximately calculated as
⌬SM共T,H0兲=
␮
0兺
i
Mi+1共Ti+1,H兲−Mi共Ti,H兲
Ti+1 −Ti
⌬H.共3兲
On the other hand, ⌬SMcan be obtained from calorimet-
ric measurements of the field dependence of the heat capac-
ity and subsequent integration,
⌬SM共T,H0兲=
冕
0
TC共T,H兲−C共T,0兲
TdT,共4兲
where C共T,H0兲and C共T,0兲are the values of the heat capac-
ity measured in the field H0and in zero field 共H=0兲, respec-
tively. Therefore, the adiabatic temperature change 共⌬Tad兲
can be evaluated by integrating Eq. 共4兲over the magnetic
field, which is given by
⌬Tad共T,H0兲=
␮
0
冕
0
H0
冉
T
C共T,H兲⫻
⳵
M共T,H兲
⳵
T
冊
H
dH.共5兲
By taking Eq. 共2兲into account, the adiabatic temperature
change 共⌬Tad兲at an arbitrary temperature T0can be approxi-
mately calculated by
⌬Tad共T0,H0兲⬵−⌬SM共T0,H0兲T0
C共T0,H0兲.共6兲
The RC of a magnetic refrigerant material is calculated as10
RC = −
冕
T1
T2
⌬SM共T兲dT,共7兲
which indicates how much heat can be transferred from the
cold end 共at T1兲to the hot end 共at T2兲of a refrigerator in an
ideal thermodynamic cycle.
We note from Eq. 共2兲that the magnitude of ⌬SMdepends
on both the magnitude of the magnetization 共M兲and
共
⳵
M/
⳵
T兲H. The larger these values, the larger the magnitude
of ⌬SM.13 Since 共
⳵
M/
⳵
T兲His related to the magnetic order-
ing transition, the sharper change in Mwith respect to tem-
perature at the transition temperature leads to the larger
⌬SM.14,15 According to Eq. 共6兲, at the same temperature the
large ⌬Tad is achieved as the ⌬SMis large and the C共T,H兲is
small. Since the magnitude of C共T,H兲varies from one ma-
terial to another, large ⌬SMdoes not necessarily lead to the
large ⌬Tad.10 Therefore, only using the magnitude of ⌬SMto
assess the usefulness of a magnetic refrigerant material is
inadequate. Instead, a more appropriate way to do this is to
calculate the RC from Eq. 共7兲, which takes into account both
the magnitude of ⌬SMand the temperature response of
⌬SM.10–12
III. EXPERIMENT
Polycrystals of Pr0.5Sr0.5MnO3were fabricated from
Pr2O3, SrCO3, and MnO using standard solid-state reaction
methods. The starting powders were thoroughly ground and
then reacted in air for 10 days at 1500 °C with several in-
termediate grindings. The reacted powders were then cold
pressed into disks of 1.5 mm thickness and sintered in air for
1 day at 1500 ° C. The final sintered samples were slow
cooled over a period of 40 h to room temperature. Structural
characterization was performed by x-ray powder diffraction,
confirming structure 共orthorhombic兲and lattice parameters
similar to those in prior work.
Magnetic measurements were performed using a com-
mercial Physical Property Measurement System from Quan-
tum Design in the temperature range of 5–300 K at applied
fields up to 7 T. The magnetization isotherms were measured
with a field step of 0.05 mT in the range of 0–5 T and with a
temperature interval of 3 K over a temperature range of
5–300 K.
IV. RESULTS AND DISCUSSION
Figure 1共a兲shows the temperature dependence of zero-
field-cooled 共ZFC兲and field-cooled 共FC兲magnetizations
FIG. 1. 共Color online兲共a兲Temperature dependence of ZFC and FC magne-
tizations taken at a field of 0.05 T. The inset shows the derivative of mag-
netization with respect to temperature 共dM/dT vs T兲. The values of TC
⬃255 K and TCO ⬃165 K are, respectively, defined by the minimum and
maximum in dM/dT. AFM/CO, FM, and PM 共paramagnetic兲.共b兲Tempera-
ture dependence of magnetization taken at different magnetic fields up to 5
T.
023909-2 Bingham et al. J. Appl. Phys. 106, 023909 共2009兲

taken at a field of 0.05 T. In agreement with prior studies,5,6
the present Pr0.5Sr0.5MnO3system undergoes a SOMT from
the paramagnetic to the FM state at TC⬃255 K followed by
a FOMT from the FM charge-disordered to AFM CO state at
TCO ⬃165 K. These transitions are well known in this mate-
rial although the values of TCand TCO extracted from the
minimum and maximum in dM/dT 关see inset of Fig. 1共a兲兴,
respectively, are slightly different from those reported in the
literature.5,16 The slightly depressed Curie temperature could
be accounted for by small nonstoichiometry, particularly
oxygen deficiency. It is also noted that Pr0.5Sr0.5MnO3is not
a usual checkerboard type CO antiferromagnet like the case
of Nd0.5Sr0.5MnO3but shows a two-dimensional anisotropic
AFM and charge ordering insulating state.17
The effect of magnetic field on the SOMT and FOMT
are further revealed from MFC共T兲curves taken in higher
magnetic fields 共
␮
0H=1,2,3,4,and5T兲, as shown in Fig.
1共b兲. It can be observed that the SOMT at TCprogressively
broadens as the magnetic field is increased, whereas the
FOMT at TCO remains reasonably sharp even at a field of up
to 5 T due to the strong coupling between the magnetism and
the lattice in the vicinity of the TCO.16 In a study reported by
Hu et al.,14 the compound MnAs0.9Sb0.1 displayed a smooth
temperature variation of the magnetization under high fields,
whereas the shape of the M-Tcurve for MnAs was almost
unchanged. As a result, MnAs exhibited a larger MCE com-
pared with MnAs0.9Sb0.1.14 In a recent study reported by
Phan et al.,18 giant MCE has been observed in a type-VIII
Eu8Ga16Ge30 clathrate in which the SOMT remains quite ro-
bust under high magnetic fields. Our experimental observa-
tion reported here leads to a similar expectation that the
Pr0.5Sr0.5MnO3manganite would show a larger change in
magnetic entropy at around TCO than around TC.
In order to evaluate the MCE, the isothermal magnetiza-
tion curves of the sample were measured with a field step of
0.05 mT in a range of 0–5 T and a temperature step of 3 K
over a range of temperatures around TCand TCO. Such fami-
lies of M共H兲curves are shown in Figs. 2共a兲and 2共b兲, respec-
tively. As expected from Fig. 1, there is a more drastic
change in the magnetization around the TCO 关see Fig. 2共b兲兴
than around the TC关see Fig. 2共a兲兴, indicating a larger mag-
netic entropy change in the vicinity of the TCO. It is worth
mentioning that around the TCO the sample shows S-shaped
magnetization, which is typical for metamagnetic
materials.19 The importance of metamagnetism for achieving
large MCE in La0.7Ca0.3−xSrxMnO3−
␦
; manganites has re-
cently been discussed by Ulyanov et al.20 The authors have
demonstrated the role of oxygen deficiency as a driving force
for the metamagnetism and large low-field MCE in these
manganites.20 For the case of Pr0.5Sr0.5MnO3, however, it is
believed that the metamagnetism arises mainly from the co-
existence of the competing AFM/CO and FM phases and the
collapse of the AFM/CO state that occurs in the presence of
an external magnetic field.16
Figure 3shows the temperature dependence of the mag-
netic entropy change 共−⌬SM兲taken at different magnetic
fields ranging from 0.15 to 5 T. Here, the −⌬SMwas calcu-
lated from a family of isothermal M共H兲curves shown in
Figs. 2共a兲and 2共b兲using Eq. 共2兲. It can be observed that the
Pr0.5Sr0.5MnO3system exhibits large magnetic entropy
changes around the TCand around the TCO. As expected from
the M共T兲and M共H兲data, the −⌬SMaround TCO is much
larger than that around TC. For ⌬
␮
0H=5 T, the magnitude
of −⌬SM共−7.5 J /kg K兲at TCO is about twice larger than that
共3.2 J/kg K兲at TC. A similar trend was also reported by
Sande et al.4on Nd0.5Sr0.5MnO3and by Chen et al.5on
Pr0.5Sr0.5MnO3. In those cases, however, attention was drawn
only to large values of −⌬SMaround TCO without any con-
sideration of the RC and hysteretic losses.4,5In the present
case, we note from Fig. 4that the large −⌬SMaround the TCO
is only sustained over a narrow temperature range, whereas
the −⌬SMaround the TCis spread over a broader temperature
range. This would lead to improved RC, which is the most
important factor for assessing the usefulness of a magnetic
refrigerant material.
FIG. 2. 共Color online兲Isothermal magnetization curves taken at different
fixed temperatures between 5 and 300 K for the Pr0.5Sr0.5MnO3manganite:
共a兲around TCand 共b兲around TCO.
FIG. 3. 共Color online兲Temperature dependence of magnetic entropy change
共−⌬SM兲at different applied fields up to 5 T for the Pr0.5Sr0.5MnO3
manganite.
023909-3 Bingham et al. J. Appl. Phys. 106, 023909 共2009兲

To address this unresolved important issue, we have cal-
culated the RC for both the cases around the TCand around
the TCO using Eq. 共7兲. Figure 4shows the method for calcu-
lating the RC from the −⌬SM共T兲curve. In this figure, the
hatched area under the −⌬SM共T兲curve corresponds to the
RC of the material in each temperature range around TCand
TCO. The upper and lower temperature limits of the shaded
area represent the temperatures of the hot and cold reservoirs
共T2and T1, respectively兲. These limiting temperatures are
obtained from the temperatures at the half maximum of the
peak value of the −⌬SM共T兲curve.12 The calculated results of
RC are plotted as a function of magnetic field and are shown
in Fig. 5. It can be observed that for both cases, the RC
increases as the magnetic field is increased. An important
fact to be emphasized here is that the magnitude of RC is
significantly larger for the case around the TCthan for the
case around the TCO for ⌬
␮
0H⬍3.7 T, which can be con-
sidered as the magnetic field range of practical importance
for refrigeration. For example, for ⌬
␮
0H=2 T, the RC is 79
J/kg for the case around the TC, while it is 70 J/kg for the
case around the TCO. As shown previously in Ref. 10,inthe
same refrigeration cycle, a material with higher RC is pre-
ferred because it would support the transport of a greater
amount of heat in a practical refrigerator. Therefore, for the
case of Pr0.5Sr0.5MnO3, the larger value of RC around the TC
indicates that magnetic refrigeration in the vicinity of the TC
is more effective than that around the TCO.
Furthermore, we recall that hysteretic losses 共magnetic
and thermal hystereses兲are often involved in FOMT,19 which
would again justify the calculated RC values. Because these
hysteretic losses are the costs in energy to make one cycle of
the magnetic field, they must be considered when calculating
the usefulness of a magnetic refrigerant material being sub-
jected to field cycling.11 To evaluate possible hysteretic
losses involved in the magnetic phase transitions in
Pr0.5Sr0.5MnO3, we measured the M-Hcurves at tempera-
tures around the TCand the TCO. The inset of Fig. 5shows,
for example, the M共H兲curves measured at 180 K 共below TC兲
and at 150 K 共below TCO兲. It can be seen that the hysteretic
losses 共the area is composed of the increasing and decreasing
field curves兲are very large below the TCO, whereas they are
very small or negligible below the TC. To be precise, we have
subtracted the average hysteretic losses from the RC values
calculated without accounting for the hysteretic losses. For
comparison, the results of RC after subtracting the average
hysteretic losses for the case around the TCO are also in-
cluded in Fig. 5. It can be observed in Fig. 5that in the range
of magnetic fields investigated, the RC around the TCis
much larger than that around the TCO. For example, for a
change in magnetic field of 5 T, the RC is 215 J/kg for the
case around the TC, while it is 168 J/kg for the case around
the TCO. This clearly indicates that such hysteretic losses
involved in FOMT significantly reduce the RC and are there-
fore undesirable for an efficient magnetic refrigeration cycle.
An important fact that emerges from the present study is
that the comparison of MCE among magnetocaloric materi-
als by considering the magnitude of ⌬SMonly is not ideal.4,5
Instead, a proper estimation should be made with the use of
RC, paying attention to the fact that magnetic hysteresis
losses must be estimated and subtracted from the RC calcu-
lation. In addition, this comparison should be made in the
same temperature range. From a magnetocaloric material
perspective, it is believed that not only FOMT materials but
also SOMT materials are promising candidates for active
magnetic refrigeration applications. Some SOMT materials
with zero hysteretic losses are even more advantageous. An
example of this is Gd—the best magnetic refrigerant candi-
date material to date for sub-room-temperature magnetic
refrigeration.21 Considering the fact that SOMT materials
with a large magnetic entropy change over a broad tempera-
ture range usually possess large RC,13,21 it could be worth-
while to search for enhanced RC in materials that undergo
multiple magnetic phase transitions.22–24 From this perspec-
tive, MCE in composite magnetic materials with multiple
SOMTs may be of great interest.22
V. CONCLUSIONS
We have studied the influence of first- and second-order
magnetic phase transitions on the MCE and RC of CO
Pr0.5Sr0.5MnO3. It is shown that while the FOMT at TCO
results in a larger MCE in terms of magnitude, the peak is
confined to a narrow temperature region. The SOMT at TC
yields a smaller MCE with a broader peak spanning a wider
temperature range. This results in a larger value of the RC
around TC, which is more useful for practical applications.
FIG. 4. 共Color online兲The method for calculating the RC from the −⌬SM共T兲
curve using Eq. 共7兲for the cases around TCand TCO.
FIG. 5. 共Color online兲Magnetic field dependence of RC calculated using
Eq. 共7兲for the cases around TCand TCO 共without and with subtracted hys-
teretic losses兲. The inset shows the magnetic field dependence of magneti-
zation taken 共a兲at 150 K 共below TCO兲and 共b兲at 180 K 共below TC兲.
023909-4 Bingham et al. J. Appl. Phys. 106, 023909 共2009兲

Hysteretic losses accompanying the FOMT are very large
below TCO and therefore detrimental to the RC, whereas they
are negligible below TCdue to the nature of the SOMT. A
proper comparison between magnetocaloric materials should
be made with the use of RC, paying attention to the fact that
magnetic hysteretic losses must be estimated and subtracted
from the RC calculation.
AKNOWLEDGMENTS
The authors acknowledge work at USF supported by
DOE BES Physical Behavior of Materials Program through
Grant No. DE-FG02-07ER46438. H.S. also acknowledges
support from USAMRMC through Grant No. W81XWH-07-
1-0708. Work at UMN supported primarily by DOE 共Grant
No. DE-FG02-06ER46275兲and NSF 共Grant No. DMR-
0804432兲is also acknowledged.
1Y. Tokura and Y. Tomioka, J. Magn. Magn. Mater. 200,1共1999兲.
2M. H. Phan and S. C. Yu, J. Magn. Magn. Mater. 308, 325 共2007兲.
3A. M. Tishin and Y. I. Spichkin, The Magnetocaloric Effect and Its Appli-
cations 共Institute of Physics, Bristol, 2003兲.
4P. Sande, L. E. Hueso, D. R. Miguens, J. Rivas, F. Rivadulla, and M. A.
Lopez-Quintela, Appl. Phys. Lett. 79, 2040 共2001兲.
5P. Chen, Y. W. Du, and G. Ni, Europhys. Lett. 52,589共2000兲.
6M. S. Reis, V. S. Amaral, J. P. Araujo, P. B. Tavares, A. M. Gomes, and I.
S. Oliveira, Phys. Rev. B 71, 144413 共2005兲.
7R. Venkatesh, M. Pattabiraman, K. Sethupathi, G. Rangarajan, and S. N.
Jammalamadaka, J. Appl. Phys. 101, 09C506 共2007兲.
8S. Karmakar, E. Bose, S. Taran, B. K. Chauhuri, C. P. Sun, and H. D.
Yang , J. Appl. Phys. 103, 023901 共2008兲.
9A. Biswas, T. Samanta, S. Banerjee, and I. Das, Appl. Phys. Lett. 92,
012502 共2008兲.
10V. K. Pecharsky and K. A. Gschneidner, Jr., J. Appl. Phys. 90, 4614
共2001兲.
11V. Provenzano, A. J. Shapiro, and R. D. Shull, Nature 共London兲429,853
共2004兲.
12V. K. Sharma, M. K. Chattopadhyay, and S. B. Roy, J. Phys. D: Appl.
Phys. 40, 1869 共2007兲.
13O. Tegus, E. Bruck, L. Zhang, Dagula, K. H. J. Buschow, and F. R. de
Boer, Physica B 319, 174 共2002兲.
14F. X. Hu, B. G. Shen, and J. R. Sun, Appl. Phys. Lett. 76,3460共2000兲.
15M. H. Phan, S. C. Yu, and N. H. Hur, Appl. Phys. Lett. 86, 072504 共2005兲.
16Y. Tomioka, A. Asamitsu, Y. Moritomo, H. Kuwahara, and Y. Tokura,
Phys. Rev. Lett. 74, 5108 共1995兲.
17H. Kawano, R. Kajimoto, H. Yoshizawa, Y. Tomioka, H. Kuwahara, and
Y. Tokura, Phys. Rev. Lett. 78, 4253 共1997兲.
18M. H. Phan, G. T. Woods, A. Chaturvedi, S. Stefanoski, G. S. Nolas, and
H. Srikanth, Appl. Phys. Lett. 93, 252505 共2008兲.
19S. B. Roy, P. Chaddah, V. K. Pecharsky, and K. A. Gschneidner, Jr., Acta
Mater. 56, 5895 共2008兲.
20A. N. Ulyanov, J. S. Kim, Y. M. Kang, D. G. Yoo, and S. I. Yoo, J. Appl.
Phys. 104, 113916 共2008兲.
21V. K. Pecharsky and K. A. Gschneidner, Jr., J. Magn. Magn. Mater. 200,
44 共1999兲.
22P. Kumar, N. K. Singh, K. G. Suresh, and A. K. Nigam, Phys. Rev. B 77,
184411 共2008兲.
23A. Biswas, T. Samanta, S. Banerjee, and I. Das, J. Appl. Phys. 103,
013912 共2008兲.
24S. Gorsse, B. Chevalier, and G. Orveillon, Appl. Phys. Lett. 92, 122501
共2008兲.
023909-5 Bingham et al. J. Appl. Phys. 106, 023909 共2009兲